RESEARCH ARTICLES CURRENT SCIENCE, VOL. 107, NO. 11, 10 DECEMBER 2014 1842 *For correspondence. (e-mail: sujaybandyopadhyayest@gmail.com) Entropy application to evaluate the stability of landscape in Kunur River Basin, West Bengal, India Sujay Bandyopadhyay 1, *, Subhajit Sinha 2 , N. C. Jana 1 and Debasis Ghosh 3 1 Department of Geography, The University of Burdwan, Golapbag, Burdwan 713 104, India 2 Post-Graduate Department of Geology, Durgapur Government College, Durgapur 713 214, India 3 Department of Geography, Sidho-Kanho-Birsha University, Purulia 723 101, India The river network analysis using thermodynamic entropy approach has been studied over the past sev- eral decades to decipher the behaviour of streams and landscape stability. The entropy-based study has been taken up in Kunur River Basin of eastern India to ver- ify the level of adjustment for its present longitudinal profile to the calculated and equilibrium longitudinal profiles adopting Yang’s (1971) theory of average river fall. The verification reveals that the fall ratio is less than 1, which indicates the basin has not yet reached the dynamic equilibrium phase and the whole process–response system sustains tremendous human pressure. It is inferred from the thermodynamic river profiles that there is poor agreement between ob- served data and the law of average stream fall, and the concave river profile emerging from several scales of process-form interaction is characterized by human interference. The present analyses also demonstrate that the lithological control, grain size and channel morphology influence the gradient in short term and climate-induced hydrological changes control the long-term stability of the total landscape. Keywords: Dynamic equilibrium, landscape stability, longitudinal profile, potential energy, thermodynamic entropy. CONSIDERABLE geomorphic and hydrological research on drainage network analysis using thermodynamic approach has addressed the concept of dynamic balance that guides the fluvial system 1–4 . Entropy is important to understand the landscape evolution through the distribution of availa- ble potential energy. It is the only useful energy in stream morphology provided by nature that gives over- land flow and converts into kinetic energy when the unit mass of water is flowing downstream 1,3 . Using this gen- erated kinetic energy, the flow can carve its own channel and form the stream network. During the channel forma- tion, the river shapes up the channel pattern and the longi- tudinal profiles of the waterways. With continued erosion, the features of the landscape change with the change in topography. Thus the noticeable information available on a drainage basin is its mean elevation 4 , implying the connection between entropy and potential energy. The drainage basin morphological characteristics have been analysed because the shape of all streams observed today should be the cumulated result of the distribution and expenditure of potential energy along their course of flow throughout the past. The variation and distribution of potential energy loss per unit mass of flow have a power- ful effect on the stream network and it is proportional to the vertical fall between the source and the confluence. In this context, Yang 3 developed the analogy equation H  = Y  , (1) where H  is the average loss of potential energy by unit mass of water for all water courses of the order , Y  is the fall (level difference) between the source and mouth of the water course of order  and  is a factor for con- version between energy and fall. Adapting the concepts of thermo-mechanics analogy, i.e. the entropy variation of a fluvial system d / , m m S H Z    (2) where H m is the total average potential energy loss per unit mass of water from the source to the confluence of mth order stream and Z m is the total fall from the begin- ning of the first-order stream to the end of the mth order stream of Leopold and Langbein 1 , the law of average fall equality ( Y  = Y +1 = constant) has been developed by Yang 3 when a river system has reached a condition of dynamic equilibrium. Here the thermal energy in a ther- mal system is equivalent to potential energy for the fluvial network and the absolute temperature is equiva- lent to elevation in a river system. The use of this analogy in a fluvial system is considered to be an open thermody- namic system, justified and empirically established by Scheidegger 2,5 . On the other hand, methodological base of the Yang’s law of average fall equality is founded on the Prigogine 6 theorem for a classic thermodynamic system